English
Maharashtra State BoardSSC (English Medium) 9th Standard

Solve the following simultaneous equation. x - 2y = - 2 ; x + 2y = 10 - Algebra

Advertisements
Advertisements

Question

Solve the following simultaneous equation.

x − 2y = −2 ; x + 2y = 10 

Sum
Advertisements

Solution

x − 2y = −2    ...(I)

x + 2y = 10    ...(II)

Adding (I) and (II)

    x − 2y = −2
+ x + 2y = 10 
    2x = 8

⇒ x = 4

Putting the value of x in (I) we get

∴ x - 2y = −2

⇒ 4 − 2y = −2

⇒ −2y = −6

⇒ y = 3

shaalaa.com
  Is there an error in this question or solution?
Chapter 5: Linear Equations in Two Variables - Problem Set 5 [Page 91]

APPEARS IN

Balbharati Mathematics 1 [English] Standard 9 Maharashtra State Board
Chapter 5 Linear Equations in Two Variables
Problem Set 5 | Q (2) (vi) | Page 91

RELATED QUESTIONS

Solve the following system of linear equations by applying the method of elimination by equating the coefficients

(i)4x – 3y = 4 

2x + 4y = 3

(ii)5x – 6y = 8

3x + 2y = 6


Solve the following system of linear equations by using the method of elimination by equating the coefficients: 3x + 4y = 25 ; 5x – 6y = – 9


Solve the following system of equations: 15x + 4y = 61; 4x + 15y = 72


Solve for x and y : `\frac { ax }{ b } – \frac { by }{ a } = a + b ; ax – by = 2ab`


Solve (a – b) x + (a + b) y = `a^2 – 2ab – b^2 (a + b) (x + y) = a^2 + b^2`


Form the pair of linear equation in the following problem, and find its solution (if they exist) by the elimination method:

Meena went to a bank to withdraw ₹ 2000. She asked the cashier to give her ₹ 50 and ₹ 100 notes only. Meena got 25 notes in all. Find how many notes of ₹ 50 and ₹ 100 she received.


Sanjay gets fixed monthly income. Every year there is a certain increment in his salary. After 4 years, his monthly salary was Rs. 4500 and after 10 years his monthly salary became 5400 rupees, then find his original salary and yearly increment.


The sum of the digits in a two-digits number is 9. The number obtained by interchanging the digits exceeds the original number by 27. Find the two-digit number.


If the length of a rectangle is reduced by 5 units and its breadth is increased by 3 units, then the area of the rectangle is reduced by 9 square units. If length is reduced by 3 units and breadth is increased by 2 units, then the area of rectangle will increase by 67 square units. Then find the length and breadth of the rectangle.


By equating coefficients of variables, solve the following equation.

5x + 7y = 17 ; 3x - 2y = 4


By equating coefficients of variables, solve the following equation.

x − 2y = −10 ; 3x − 5y = −12


The difference between an angle and its complement is 10° find measure of the larger angle.


Complete the following table to draw the graph of 3x − 2y = 18

x 0 4 2 −1
y − 9 ______ ______ ______
(x, y) (0, −9) (______, _______) (______, _______) ______

Difference between two numbers is 3. The sum of three times the bigger number and two times the smaller number is 19. Then find the numbers


Solve: 99x + 101y = 499, 101x + 99y = 501


A 2-digit number is such that the product of its digits is 24. If 18 is subtracted from the number, the digits interchange their places. Find the number.


Read the following passage:

Two schools 'P' and 'Q' decided to award prizes to their students for two games of Hockey ₹ x per student and Cricket ₹ y per student. School 'P' decided to award a total of ₹ 9,500 for the two games to 5 and 4 Students respectively; while school 'Q' decided to award ₹ 7,370 for the two games to 4 and 3 students respectively.

Based on the above information, answer the following questions:

  1. Represent the following information algebraically (in terms of x and y).
  2. (a) What is the prize amount for hockey?
    OR
    (b) Prize amount on which game is more and by how much?
  3. What will be the total prize amount if there are 2 students each from two games?

Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×